Real Rate of Return worksheet

1. Nominal return needed: 7.12%

1. Multiply the growth you want (1 + real return) by the growth in prices (1 + inflation), then subtract 1, so both kinds of growth are covered

   $\left(1+0.04\right)\times \left(1+0.03\right)-1$$=0.0712$

2. Write the decimal as a percent

   $0.0712\times 100$$=\mathrm{7.12\%}$

3. Grow the amount at the stated rate for 8 years to get future dollars

   $\mathrm{\$11,750.00}\times {\left(1+0.0712\right)}^8$$=\mathrm{\$20,370.53}$

4. Grow it at the real rate instead to see what it's worth in today's buying power

   $\mathrm{\$11,750.00}\times {\left(1+0.04\right)}^8$$=\mathrm{\$16,080.69}$

2. Real rate of return: 3.8835%

1. Divide your money's growth (1 + stated return) by the growth in prices (1 + inflation), then subtract 1. This is the Fisher equation

   $\frac{1+0.07}{1+0.03}-1$$=0.03883495$

2. Write the decimal as a percent

   $0.03883495\times 100$$=\mathrm{3.883495\%}$

3. For comparison, the quick estimate just subtracts inflation, which slightly overstates the real return

   $\mathrm{7\%}-\mathrm{3\%}$$=\mathrm{4\%}$

4. Grow the amount at the stated rate for 11 years to get future dollars

   $\mathrm{\$9,000.00}\times {\left(1+0.07\right)}^{11}$$=\mathrm{\$18,943.67}$

5. Grow it at the real rate instead to see what it's worth in today's buying power

   $\mathrm{\$9,000.00}\times {\left(1+0.03883495\right)}^{11}$$=\mathrm{\$13,685.31}$

3. Break-even inflation rate: 4.8544%

1. Divide your money's growth (1 + stated return) by the growth you want (1 + real return), then subtract 1. What's left is the inflation it can absorb

   $\frac{1+0.08}{1+0.03}-1$$=0.04854369$

2. Write the decimal as a percent

   $0.04854369\times 100$$=\mathrm{4.854369\%}$

3. Grow the amount at the stated rate for 10 years to get future dollars

   $\mathrm{\$10,000.00}\times {\left(1+0.08\right)}^{10}$$=\mathrm{\$21,589.25}$

4. Grow it at the real rate instead to see what it's worth in today's buying power

   $\mathrm{\$10,000.00}\times {\left(1+0.03\right)}^{10}$$=\mathrm{\$13,439.16}$

4. Break-even inflation rate: 0.9434%

1. Divide your money's growth (1 + stated return) by the growth you want (1 + real return), then subtract 1. What's left is the inflation it can absorb

   $\frac{1+0.07}{1+0.06}-1$$=0.00943396$

2. Write the decimal as a percent

   $0.00943396\times 100$$=\mathrm{0.943396\%}$

3. Grow the amount at the stated rate for 12 years to get future dollars

   $\mathrm{\$11,600.00}\times {\left(1+0.07\right)}^{12}$$=\mathrm{\$26,125.42}$

4. Grow it at the real rate instead to see what it's worth in today's buying power

   $\mathrm{\$11,600.00}\times {\left(1+0.06\right)}^{12}$$=\mathrm{\$23,341.48}$

5. Break-even inflation rate: 2.8846%

1. Divide your money's growth (1 + stated return) by the growth you want (1 + real return), then subtract 1. What's left is the inflation it can absorb

   $\frac{1+0.07}{1+0.04}-1$$=0.02884615$

2. Write the decimal as a percent

   $0.02884615\times 100$$=\mathrm{2.884615\%}$

3. Grow the amount at the stated rate for 9 years to get future dollars

   $\mathrm{\$8,000.00}\times {\left(1+0.07\right)}^9$$=\mathrm{\$14,707.67}$

4. Grow it at the real rate instead to see what it's worth in today's buying power

   $\mathrm{\$8,000.00}\times {\left(1+0.04\right)}^9$$=\mathrm{\$11,386.49}$

6. Break-even inflation rate: 1.9417%

1. Divide your money's growth (1 + stated return) by the growth you want (1 + real return), then subtract 1. What's left is the inflation it can absorb

   $\frac{1+0.05}{1+0.03}-1$$=0.01941748$

2. Write the decimal as a percent

   $0.01941748\times 100$$=\mathrm{1.941748\%}$

3. Grow the amount at the stated rate for 11 years to get future dollars

   $\mathrm{\$7,000.00}\times {\left(1+0.05\right)}^{11}$$=\mathrm{\$11,972.38}$

4. Grow it at the real rate instead to see what it's worth in today's buying power

   $\mathrm{\$7,000.00}\times {\left(1+0.03\right)}^{11}$$=\mathrm{\$9,689.64}$

7. Nominal return needed: 9.18%

1. Multiply the growth you want (1 + real return) by the growth in prices (1 + inflation), then subtract 1, so both kinds of growth are covered

   $\left(1+0.06\right)\times \left(1+0.03\right)-1$$=0.0918$

2. Write the decimal as a percent

   $0.0918\times 100$$=\mathrm{9.18\%}$

3. Grow the amount at the stated rate for 11 years to get future dollars

   $\mathrm{\$9,000.00}\times {\left(1+0.0918\right)}^{11}$$=\mathrm{\$23,649.20}$

4. Grow it at the real rate instead to see what it's worth in today's buying power

   $\mathrm{\$9,000.00}\times {\left(1+0.06\right)}^{11}$$=\mathrm{\$17,084.69}$

8. Break-even inflation rate: 4.8544%

1. Divide your money's growth (1 + stated return) by the growth you want (1 + real return), then subtract 1. What's left is the inflation it can absorb

   $\frac{1+0.08}{1+0.03}-1$$=0.04854369$

2. Write the decimal as a percent

   $0.04854369\times 100$$=\mathrm{4.854369\%}$

3. Grow the amount at the stated rate for 10 years to get future dollars

   $\mathrm{\$12,000.00}\times {\left(1+0.08\right)}^{10}$$=\mathrm{\$25,907.10}$

4. Grow it at the real rate instead to see what it's worth in today's buying power

   $\mathrm{\$12,000.00}\times {\left(1+0.03\right)}^{10}$$=\mathrm{\$16,127.00}$

9. Real rate of return: 4.902%

1. Divide your money's growth (1 + stated return) by the growth in prices (1 + inflation), then subtract 1. This is the Fisher equation

   $\frac{1+0.07}{1+0.02}-1$$=0.04901961$

2. Write the decimal as a percent

   $0.04901961\times 100$$=\mathrm{4.901961\%}$

3. For comparison, the quick estimate just subtracts inflation, which slightly overstates the real return

   $\mathrm{7\%}-\mathrm{2\%}$$=\mathrm{5\%}$

4. Grow the amount at the stated rate for 12 years to get future dollars

   $\mathrm{\$9,750.00}\times {\left(1+0.07\right)}^{12}$$=\mathrm{\$21,958.87}$

5. Grow it at the real rate instead to see what it's worth in today's buying power

   $\mathrm{\$9,750.00}\times {\left(1+0.04901961\right)}^{12}$$=\mathrm{\$17,314.42}$

10. Nominal return needed: 7.12%

1. Multiply the growth you want (1 + real return) by the growth in prices (1 + inflation), then subtract 1, so both kinds of growth are covered

   $\left(1+0.04\right)\times \left(1+0.03\right)-1$$=0.0712$

2. Write the decimal as a percent

   $0.0712\times 100$$=\mathrm{7.12\%}$

3. Grow the amount at the stated rate for 12 years to get future dollars

   $\mathrm{\$9,500.00}\times {\left(1+0.0712\right)}^{12}$$=\mathrm{\$21,685.55}$

4. Grow it at the real rate instead to see what it's worth in today's buying power

   $\mathrm{\$9,500.00}\times {\left(1+0.04\right)}^{12}$$=\mathrm{\$15,209.81}$